Ok, I'll play: I don't see how you could accurately estimate that., You would need to know the causal mechanism for the 10.1% Serious Adverse Events (SAE) in the original treatment group. If it was caused by a particular genetic condition (i.e. MTHFR), then it could be less than 10.1% once you exclude those removed from the treatment group. But it could easily be a dose response effect as well and that could result in a SAE greater than 10.1%. Even this ignores that some SAEs could take longer to show up in the treatment group, so it would depend on follow up times, etc.
EDITED to add: Math cannot do more than generate an estimate based on certain assumptions. That's why the trail must actually be run. However, if we assume that the 89,900 who get the second shot have a 10.1% SAE rate (a very big assumption), then that's 9080 people in the second dose group who have an SAE. Add to this the 10,100 people from the first dose yields 19,180 people out of the original 100,000, or 19.18%.
Using the same assumptions, if you run a third round on the remaining 80,820 with no SAEs adds another 8163 people to the SAE pool, creating an overall SAE of 27.343%
Agreed. We know that the products in general showed higher SAEs for dose 2. And as you point, some people who were highly prone to have bad reactions would drop after first dose. If I were approaching this as calling for a Fermi-type estimate, I would say the two opposing factors cancel each other out and use 10.1% for each vaccination event for purposes of this exercise.
Impossible to compute because the second booster will have, no doubt, an increased negative effect, maybe more than double the bad side effects of the first booster. Let's just stick with the monkeypox.
I believe Mr. Lyons-Weiler is asking what is the probability of a SAE from either dose 1 or dose 2 (booster). So to compare to coin flips, the question is what is the probability that in two flips, at least one will be heads? For coin flips, the probability is 75% that in two coin flips, at least one will be heads.
Where the probability of SAE is 10.1%, the answer is 19.18%. In essence a 1 in 5 chance of an SAE over two injections.
*[Edit to change 19.8 to 19.18%]*
Formula where there are n trials:
P(at least one success) = 1 - P(failure in one trial)ⁿ
24-HR QUIZ QUESTION: What will the unbiased SAE population rate be for the booster in the second exposure?
Math is my nemesis so my first thought is has Mathew Crawford done the calculation; there's got to be some fancy multiplier that goes with instinctive element that the second is at least twice as bad as the first one. Then again this is a vaccinologist formula so it's probably wrong and my guess will be in good company and make all he folks who do math sigh, get a CDC job!
If nothing else it is an example of how average folks get snookered & confused with percentage figures and it's teachable moment for how not to calculate properly. :~)
Second exposure: N=100,00-10,100 = 89,900
Reported SAE rate (if unbiased): 10.1%
89,900 x 10.1% = 898.9
89,900 - 898.9 = 88, 101
AE total doses 1&2 (10,100 + 898.9 = 10,998.9)
It feels tricky here.. what denominator? Where's Mathew now?
10,999/100,000 = 10.99% barely a difference for total AE/ full group
10,999/89,101 = 12.3% total AE /unharmed group
Final answer with instinct bias & high uncertainty 12.3%
I think there is a problem in how you phrased this. That 10% of your population are 'at risk for' an adverse reaction doesn't tell me that 10% actually had one. I'd also have assumed that the 0.1% of the population who had such a bad reaction to the treatment that they ended up in hospital would be included in the max 10% who were at risk for an adverse reaction. They sure got one.
At this point I cannot tell how many people are going to get sick from a second injection. If the same 10% that were at risk the first time are the ones who are at risk the second time -- i.e. it is something about them that makes them at risk, which doesn't change over time -- then the answer is, at max, all those people who were at risk the last time but but got lucky and did not have an adverse reaction.
But if the 10% is purely random, it is a problem with your vaccine which just does this to 10% of the people, then everybody is facing the same odds again. And if the problem is that the thing is cumulative you could have way more than 10% at risk. If the problem is that it is only dangerous to people with certain conditions, for instance pregnancy, you need to measure how many people develop these conditions. But by now you would have known not to vaccinate pregnant women, so .
Nobody should take the booster because SAE on first exposure is too high. And original product should be removed based upon this, as well. This is especially important if said product has not been FDA approved and is being disseminated using an EUA.
Thank you for showing your enthusiasm by participating in the commentary. Good/bad/indifferent... it all matters.
Serious Adverse Events.
No, thank you, I decline.
Serious Adverse Events
10.1%?
25%
Ok, I'll play: I don't see how you could accurately estimate that., You would need to know the causal mechanism for the 10.1% Serious Adverse Events (SAE) in the original treatment group. If it was caused by a particular genetic condition (i.e. MTHFR), then it could be less than 10.1% once you exclude those removed from the treatment group. But it could easily be a dose response effect as well and that could result in a SAE greater than 10.1%. Even this ignores that some SAEs could take longer to show up in the treatment group, so it would depend on follow up times, etc.
EDITED to add: Math cannot do more than generate an estimate based on certain assumptions. That's why the trail must actually be run. However, if we assume that the 89,900 who get the second shot have a 10.1% SAE rate (a very big assumption), then that's 9080 people in the second dose group who have an SAE. Add to this the 10,100 people from the first dose yields 19,180 people out of the original 100,000, or 19.18%.
Using the same assumptions, if you run a third round on the remaining 80,820 with no SAEs adds another 8163 people to the SAE pool, creating an overall SAE of 27.343%
Agreed. We know that the products in general showed higher SAEs for dose 2. And as you point, some people who were highly prone to have bad reactions would drop after first dose. If I were approaching this as calling for a Fermi-type estimate, I would say the two opposing factors cancel each other out and use 10.1% for each vaccination event for purposes of this exercise.
Impossible to compute because the second booster will have, no doubt, an increased negative effect, maybe more than double the bad side effects of the first booster. Let's just stick with the monkeypox.
SAE(2) = 0.11 x 2 = 0.22 => 22%
Wouldn't your formula be 0.101 x 2 = 0.202, or 20.2%?
Yes. Thanks.
Would it not still be 10.1% of the remaining population, 89,900?
I believe Mr. Lyons-Weiler is asking what is the probability of a SAE from either dose 1 or dose 2 (booster). So to compare to coin flips, the question is what is the probability that in two flips, at least one will be heads? For coin flips, the probability is 75% that in two coin flips, at least one will be heads.
Where the probability of SAE is 10.1%, the answer is 19.18%. In essence a 1 in 5 chance of an SAE over two injections.
*[Edit to change 19.8 to 19.18%]*
Formula where there are n trials:
P(at least one success) = 1 - P(failure in one trial)ⁿ
And if the rate is the same across four shots, the chances of an SAE are higher than 1 in 3! (34.68%).
Good point. Sadistics was never one of my strong subjects.
Heh, well I didn't answer Dr. Lyons-Weiler's question. I just took 10.1% across all events.
You folks are way better at math than me! Are you going to tell us the answer?
Yes, tomorrow at 11:11AM in a new article.
Isn't 0% if they all have been removed from the population? (I feeling stupid here but this is what my brain came up with)
First exposure: N=100,000
Drop-out or reported SAE: 10,100
Reported SAE rate (if unbiased): 10.1%
Second exposure: N=100,00-10,100 = 89,900
24-HR QUIZ QUESTION: What will the unbiased SAE population rate be for the booster in the second exposure?
Math is my nemesis so my first thought is has Mathew Crawford done the calculation; there's got to be some fancy multiplier that goes with instinctive element that the second is at least twice as bad as the first one. Then again this is a vaccinologist formula so it's probably wrong and my guess will be in good company and make all he folks who do math sigh, get a CDC job!
If nothing else it is an example of how average folks get snookered & confused with percentage figures and it's teachable moment for how not to calculate properly. :~)
Second exposure: N=100,00-10,100 = 89,900
Reported SAE rate (if unbiased): 10.1%
89,900 x 10.1% = 898.9
89,900 - 898.9 = 88, 101
AE total doses 1&2 (10,100 + 898.9 = 10,998.9)
It feels tricky here.. what denominator? Where's Mathew now?
10,999/100,000 = 10.99% barely a difference for total AE/ full group
10,999/89,101 = 12.3% total AE /unharmed group
Final answer with instinct bias & high uncertainty 12.3%
89,900 x 10.1% = 9079.9
Proof math is my nemesis thanks! :~)
I think there is a problem in how you phrased this. That 10% of your population are 'at risk for' an adverse reaction doesn't tell me that 10% actually had one. I'd also have assumed that the 0.1% of the population who had such a bad reaction to the treatment that they ended up in hospital would be included in the max 10% who were at risk for an adverse reaction. They sure got one.
At this point I cannot tell how many people are going to get sick from a second injection. If the same 10% that were at risk the first time are the ones who are at risk the second time -- i.e. it is something about them that makes them at risk, which doesn't change over time -- then the answer is, at max, all those people who were at risk the last time but but got lucky and did not have an adverse reaction.
But if the 10% is purely random, it is a problem with your vaccine which just does this to 10% of the people, then everybody is facing the same odds again. And if the problem is that the thing is cumulative you could have way more than 10% at risk. If the problem is that it is only dangerous to people with certain conditions, for instance pregnancy, you need to measure how many people develop these conditions. But by now you would have known not to vaccinate pregnant women, so .
I need more information.
Hi, Laura: The question states that 10.1% of the study group HAD an SAE ("reported SAE"), and 0.1% of those died. I hope this helps.
When a virus poses little to no danger for 99.9% of the population no serious injection risk is prudent.
another 10.1% or 89000 less 9009=88991
Insufficient information, but more than 10.1%.
Nobody should take the booster because SAE on first exposure is too high. And original product should be removed based upon this, as well. This is especially important if said product has not been FDA approved and is being disseminated using an EUA.